Optimal decay of the Boltzmann equation
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DOI: 10.1002/mma.10562
Abstract: The Boltzmann equation is a typical example of partially dissipative equations, where the linearized collision operator is positive definite with respect to the microscopic part and the dissipation of the hydrodynamic part is discovered from… read more here.
Keywords: optimal decay; boltzmann equation; decay; part ... See more keywords
The Boltzmann Equation for Uniform Shear Flow
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DOI: 10.1007/s00205-021-01717-5
Abstract: The uniform shear flow for the rarefied gas is governed by the time-dependent spatially homogeneous Boltzmann equation with a linear shear force. The main feature of such flow is that the temperature may increase in… read more here.
Keywords: boltzmann equation; shear flow; uniform shear;
Chapman–Enskog Analyses on the Gray Lattice Boltzmann Equation Method for Fluid Flow in Porous Media
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DOI: 10.1007/s10955-018-2005-1
Abstract: The gray lattice Boltzmann equation (GLBE) method has recently been used to simulate fluid flow in porous media. It employs a partial bounce-back of populations (through a fractional coefficient θ, which represents the fraction of… read more here.
Keywords: gray lattice; flow porous; fluid flow; boltzmann equation ... See more keywords
On Derivation of the Poisson–Boltzmann Equation
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DOI: 10.1007/s10955-020-02562-8
Abstract: Starting from the microscopic reduced Hartree–Fock equation, we derive the macroscopic linearized Poisson–Boltzmann equation for the electrostatic potential associated with the electron density. read more here.
Keywords: equation; derivation poisson; boltzmann equation; poisson boltzmann ... See more keywords
On the Derivation of the Linear Boltzmann Equation from the Nonideal Rayleigh Gas
Sign Up to like & getrecommendations! Published in 2024 at "Journal of Statistical Physics"
DOI: 10.1007/s10955-024-03353-1
Abstract: This paper’s objective is to improve the existing proof of the derivation of the Rayleigh–Boltzmann equation from the nonideal Rayleigh gas (Bodineau et al. in Invent Math 203:493–553, 2016), yielding a far faster convergence rate.… read more here.
Keywords: equation; nonideal rayleigh; rayleigh gas; equation nonideal ... See more keywords
The Linear Boltzmann Equation in Column Experiments of Porous Media
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DOI: 10.1007/s11242-020-01393-1
Abstract: The use of the linear Boltzmann equation is proposed for transport in porous media in a column. By column experiments, we show that the breakthrough curve is reproduced by the linear Boltzmann equation. The advection–diffusion… read more here.
Keywords: column experiments; boltzmann equation; linear boltzmann; equation ... See more keywords
Fixed points and flow analysis on off-equilibrium dynamics in the boson Boltzmann equation
Sign Up to like & getrecommendations! Published in 2017 at "Annals of Physics"
DOI: 10.1016/j.aop.2017.08.032
Abstract: Abstract We consider fixed points of steady solutions and flow directions using the boson Boltzmann equation that is a one-dimensionally reduced kinetic equation after the angular integration. With an elastic collision integral of the two-to-two… read more here.
Keywords: points flow; flow analysis; boltzmann equation; fixed points ... See more keywords
Error estimation and adaptive moment hierarchies for goal-oriented approximations of the Boltzmann equation
Sign Up to like & getrecommendations! Published in 2017 at "Computer Methods in Applied Mechanics and Engineering"
DOI: 10.1016/j.cma.2017.06.024
Abstract: This paper presents an a-posteriori goal-oriented error analysis for a numerical approximation of the steady Boltzmann equation based on a moment-system approximation in velocity dependence and a discontinuous Galerkin finite-element (DGFE) approximation in position dependence.… read more here.
Keywords: goal; moment; approximation; error ... See more keywords
Milne problem for the linear and linearized Boltzmann equations relevant to a binary gas mixture
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2019.12.003
Abstract: Abstract A stationary boundary-value problem for the Boltzmann equation in a half space is considered for a binary mixture of gases when the indata on the boundary are given for the both species. Under the… read more here.
Keywords: milne problem; problem linear; linearized boltzmann; boltzmann equation ... See more keywords
Space-time behavior of the solution to the Boltzmann equation with soft potentials
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2022.03.024
Abstract: Abstract. In this paper, we get the quantitative space-time behavior of the full Boltzmann equation with soft potentials (−2 < γ < 0) in the close to equilibrium setting, under some velocity decay assumption, but… read more here.
Keywords: time; time behavior; boltzmann equation; space time ... See more keywords
Global existence of solutions of the Boltzmann equation for Bose–Einstein particles with anisotropic initial data
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Functional Analysis"
DOI: 10.1016/j.jfa.2018.09.010
Abstract: In this paper we prove the global in time existence and uniqueness of solutions of the spatially homogeneous Boltzmann equation for Bose-Einstein particles for the hard sphere model for bounded anisotropic initial data. The main… read more here.
Keywords: bose einstein; boltzmann equation; equation; einstein particles ... See more keywords